A Stochastic Dynamic Program for Valuing Options on Futures

Authors

  • Mohamed A. Ayadi,

    1. Mohamed A. Ayadi is an associate professor and Robert Welch is a professor, both at the Goodman School of Business at Brock University, St. Catharines, Ontario, Canada
    Search for more papers by this author
  • Hatem Ben-Ameur,

    Corresponding author
    1. Hatem Ben-Ameur is an associate professor at the department of management sciences at HEC Montréal and a member of GERAD, Montreal, Quebec, Canada
    • Correspondence author, Department of management sciences, HEC Montréal, 3000 Chemin de la Côte-Sainte-Catherine, Montreal, Quebec, Canada, H3T 2A7. Tel: +1 514 340-6480, Fax: +1 514 340-5634, E-mail: hatem.ben-ameur@hec.ca.

    Search for more papers by this author
  • Tymur Kirillov,

    1. Tymur Kirillov is an independent consultant to CIBC, Toronto, Ontario, Canada
    Search for more papers by this author
  • Robert Welch

    1. Mohamed A. Ayadi is an associate professor and Robert Welch is a professor, both at the Goodman School of Business at Brock University, St. Catharines, Ontario, Canada
    Search for more papers by this author

  • This research is supported by Brock's internal funds for the first and fourth authors and NSERC (Canada) as well as IFM2 (Quebec) for the corresponding author. We would like to thank Don M. Chance and the JFM's anonymous referee for their comments and suggestions. They helped us to improve our paper.

Abstract

We propose a stochastic dynamic program (SDP) for valuing options on stock-index futures. SDP accommodates European- as well as American-style options, and price limits on the underlying futures contracts. Our numerical investigation shows convergence, robustness, and efficiency. SDP presents some advantages and disadvantages with respect to the binomial tree and finite differences, and stands as a viable alternative to these classic numerical methodologies for option valuation. Our empirical investigation, which focuses on American options on the S&P 500 futures contract, is almost perfect for implicit volatilities, but somewhat mitigated for historical volatilities. In volatile markets, we recommend short time windows for the volatility estimation step. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1185–1201, 2014

Ancillary